A survey is conducted in a certain neighborhood to find out residents’ favorite vacation spot. Two-fifths of the respondents, or 80 residents, said they like spending their vacation at the beach. Which equation represents the number of residents, r , surveyed? How many residents were surveyed?

Answer 1

Let \( r \) represent the total number of residents surveyed. According to the information provided, two-fifths of the respondents like spending their vacation at the beach, and this number is given as 80 residents. We can set up the equation based on this information:

\[ \frac{2}{5} r = 80 \]

To find the total number of residents surveyed, \( r \), we can solve this equation. First, we can multiply both sides by 5 to eliminate the fraction:

\[ 2r = 80 \times 5 \]

Calculating the right side:

\[ 2r = 400 \]

Now we can divide both sides by 2 to solve for \( r \):

\[ r = \frac{400}{2} \] \[ r = 200 \]

So, the total number of residents surveyed is \( \boxed{200} \).